I disagree. Integers are a property of the Universe. If you have 4 sticks, it's intrinsic in the way the Universe works that there are two groups of two.
Yes. For a silly example, one cloud and another cloud do not make two clouds, but one bigger one.
But more philosophical, it's the question of `oneness' that problematic. How can you define objects? All edges are arbitrary and if you look close enough they even blur.
(Of all the numbers the `natural' numbers are the most unnatural. Though they do describe some features of nature quite well, most scientiest would agree that e.g. complex numbers and vector fields are much more closely aligned to nature.)
Leopold Kronecker thought, "God created the integers; all the rest is the work of Man." Today we now better. The integers are no exception.
(Anyway, in practice every mathematician behaves like a Platonist no matter what his philosophical viewpoints are.)
